Question: Rewrite as a simplified fraction. ${0.3\overline{84} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 384.8484...\\ 10x &= 3.8484...\end{align*}}$ Subtracting the two equations, we have: ${990x = 381}$ ${x = \dfrac{381}{990}} $ ${x = \dfrac{127}{330}} $